Question

The sum of a man's age and his son is 66. What are their ages if the digits are reveresed ? The teacher said there are 3 answers.

Accepted Answer

Let the age of the father is presented by the 2 digit number xy.
Then, the son's age is the 2 digit number yx.
==> The fathers age = 10x + y
==. The son's age = 10y + x
But we know that the sum of their ages is 66.
==> 10x + y + 10y + x = 66
==> 11x + 11y = 66
We will divide by 11
==> x + y = 6
Then the sum of the digit must be 6.
Let us determine the positive integers whose sums are 6.
==> 0 + 6 = 6
Then the fathers age = 60
and the son's age = 06
Also, : 2 + 4 = 6
==> The father's age = 42
The son's age = 24
Also, 5 + 1 = 6
==> The fathers age = 51
The son's age = 15
Also, 3 + 3 = 6
==> The father's age = 33
The son's age = 33
But this solution is impossible because the father's and son's age can not be the same.
Then, possible answers are:
( 51 and 15 ) (24 and 42) and ( 60 and 6)

Answer

Let the man's age be ab and the son's age be ba.
Now we are given that the sum of their ages is 66.
So ab + ba = 66
=> 10a + b + 10b + a = 66
=> 11a + 11b = 66
=> a + b = 6
If a = 6 , b = 0
If a = 5, b = 1
If a = 4, b = 2
For values of a = 3 , 2 , 1 and 0 the son's age is no longer less than the man.
Therefore the age of the man and the son can be
(60, 6), (51 ,15) and (42 , 24)

Answer

Let 10x+y be the fathers age.
The sun's age is in reverse digits by data. So the sun's age = 10y+x.
Naturally father's age  is more than sun's age.
=> 10x+y > 10y +x.
=> 10x+y-10y-x > 0
=> 9x-9y > 0.
=> 9(x-y) > 0.
=> x-y > 0.
 x > y.....(1)
Also the sum of their ages = (10x+y)+(10y+x) = 11(x+y) which is 66 by data.
So 11(x+y) = 66.
We divide both sides of 11(x+y) = 66 by 11:
x+y = 6.....(2)
So x> y and x+y = 6. So we have the choice: x= 3, x= 4, x = 5, x = 6.
Then  the corresponding y values are  y= 3,  y = 2, y = 1 and y = 0.
So  father's age = 33 ,  42,  51, 60.
Sun's age : 33 , 24, 15, 06.
We exclude 33 as it is not practical.
So father and sun's age are one of the pairs:  (42 , 24) , (51, 15) , (60, 06).

Math

The sum of a man's age and his son is 66. What are their ages if the digits are reveresed ? The teacher said there are 3 answers.

Expert Answers info

Related Questions

Student Answers

Ask a Question

Popular Questions